
We perform descent calculations for the families of elliptic curves over Q with a rational point of order n=5 or 7. These calculations give an estimate for the MordellWeil rank which we relate to the parity conjecture. We exhibit explicit elements of the TateShafarevich group of order 5 and 7, and show that the 5torsion of the TateShafarevich group of an elliptic curve over Q may become arbitrarily large.